Complex dynamics of the system, revealing flutter and first presented by M. Keldysh, is analyzed in the paper in the frequency domain, through the describing function method. Motivated by this analysis, a system with similar behavior, but suitable for the exact frequency-domain analysis through the locus of a perturbed relay system (LPRS) method, is analyzed after that. The undertaken analysis shows many interesting phenomena, which include two limit cycles, orbitally stable and unstable, equilibria, and sliding mode. The undertaken analysis allows us to identify, with a high degree of confidence, the key factors leading to the complex motions in the original and transformed dynamics. © 2025 The Author(s). International Journal of Robust and Nonlinear Control published by John Wiley & Sons Ltd.